A few families took a trip to an amusement park together. Tickets cost $$6.50$ each for adults and $$4.00$ each for kids, and the group paid $$47.50$ in total. There were $4$ fewer adults than kids in the group. Find the number of adults and kids on the trip.
Solution: Let $x$ equal the number of adults and $y$ equal the number of kids. The system of equations is then: ${6.5x+4y = 47.5}$ ${x = y-4}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${y-4}$ for $x$ in the first equation. ${6.5}{(y-4)}{+ 4y = 47.5}$ Simplify and solve for $y$ $ 6.5y-26 + 4y = 47.5 $ $ 10.5y-26 = 47.5 $ $ 10.5y = 73.5 $ $ y = \dfrac{73.5}{10.5} $ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into ${x = y-4}$ to find $x$ ${x = }{(7)}{ - 4}$ ${x = 3}$ You can also plug ${y = 7}$ into ${6.5x+4y = 47.5}$ and get the same answer for $x$ ${6.5x + 4}{(7)}{= 47.5}$ ${x = 3}$ There were $3$ adults and $7$ kids.